Analysis of stresses near filleted corners

Many practical problems in civil and structural engineering involve the elastic analysis of loaded domains containing internal corners. If these corners are perfectly sharp, the stress field is singular at the point of the corner, and a crack will occur. In reality, the corners will either be designed to have a small radius (or fillet), or will be constructed with one dictated by the construction process. However, the scale of this radius will be very much smaller than the other dimensions of the structure, and so accurate analysis using the finite element method is difficult. Elements in the region of the corner must be extremely small. This paper presents an alternative approach that uses the semi-analytical scaled boundary finite-element method to connect the large-scale structure model to the small-scale model of the fillet region. The scaled boundary finite-element method is capable of modelling stresses in the region of (and indeed at) singularities, very accurately. The paper shows how advantage can be taken of this property to permit finite element modelling on a very fine scale of the fillet region, while not requiring a high level of discretisation of the rest of the structure. An example is presented illustrating this ability clearly.